I think the biggest problem with that is that time travel is very constrained. space has different properties the time like the fact that time is a one way road. For the two to look alike (confusing), the mathematical model of both entities most have several similarities. Then there is the problem of light, we see with it and our perception of the world depends on it. Since light travels the same way in your 2d world then space and time should not be mistaken.

If space is one dimensional, the force of gravity is a constant. This constant force implies constant acceleration. Constant acceleration implies constant magnitude and constant rate of change of direction. The path of motion is circular. This cyclic motion defines a quantum of time.